A bundle approach for SDPs with exact subgraph constraints
- The ‘exact subgraph’ approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational challenge because of the potentially large number of violated subgraph constraints. We introduce a computational framework for these relaxations designed to cope with these difficulties. We suggest a partial Lagrangian dual, and exploit the fact that its evaluation decomposes into two independent subproblems. This opens the way to use the bundle method from non-smooth optimization to minimize the dual function. Computational experiments on the Max-Cut, stable set and coloring problem show the efficiency of this approach.
| Author: | Elisabeth GaarGND, Franz Rendl |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/112276 |
| ISBN: | 9783030179526OPAC |
| ISBN: | 9783030179533OPAC |
| ISSN: | 0302-9743OPAC |
| ISSN: | 1611-3349OPAC |
| Parent Title (English): | Integer Programming and Combinatorial Optimization: 20th International Conference, IPCO 2019, Ann Arbor, MI, USA, May 22-24, 2019, proceedings |
| Publisher: | Springer |
| Place of publication: | Cham |
| Editor: | Andrea Lodi, Viswanath Nagarajan |
| Type: | Conference Proceeding |
| Language: | English |
| Year of first Publication: | 2019 |
| Release Date: | 2024/04/04 |
| First Page: | 205 |
| Last Page: | 218 |
| Series: | Lecture Notes in Computer Science ; 11480 |
| DOI: | https://doi.org/10.1007/978-3-030-17953-3_16 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Diskrete Mathematik, Optimierung und Operations Research | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
